Why Aren't Newtonian Gravity and General Relativity Compatible?

Newtonian gravity is not compatible with the world of special relativity.

What is wrong with Newtonian gravity? Why is general relativity better? originally appeared on Quora, the place to gain and share knowledge, empowering people to learn from others and better understand the world. You can follow Quora on Twitter, Facebook, and Google Plus.

First and foremost, Newtonian gravity is an “action-at-a-distance” theory. Newton himself was deeply concerned about this. He actually wrote (about his own theory!):

“It is inconceivable that inanimate Matter should, without the Mediation of something else, which is not material, operate upon, and affect other matter without mutual Contact…That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro' a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it. Gravity must be caused by an Agent acting constantly according to certain laws; but whether this Agent be material or immaterial, I have left to the Consideration of my readers.”

Second, Newtonian gravity is not compatible with the world of special relativity. This is a mathematical incompatibility: If you plug the equations of Newtonian gravity into the framework of special relativity, contradictions ensue.

Third, the concept of the weak equivalence principle (namely that all bodies, regardless of their material composition, respond to gravity the same way) has the important implication that at least in the immediate vicinity of a freefalling object, a simply geometric transformation can “get rid” of gravity. This suggests that the theory of gravitation has geometric origins; that is not the case with Newtonian gravity. Which, in fact, violates the weak equivalence principle in a more direct way, too, once the mass-energy equivalence of special relativity is taken into account.

Fourth, Newtonian gravity is contradicted by observation. Einstein’s three classic tests of gravity included the anomalous perihelion advance of Mercury (already known when general relativity was born, but up until that point, it had no credible explanation); the bending of light by a gravitating source like the Sun (predicting twice the value that one would get from Newtonian gravity alone, treating photons as little projectiles; confirmed by Eddington’s 1919 solar eclipse expedition); and the gravitational redshift of light (unambiguously confirmed only after Einstein’s death, in the 1950s). Since then, numerous other tests confirmed Einstein’s predictions, including precision satellite navigation or more recently, the discovery of gravitational waves.

In short, it was pretty well understood in the physics community already in the late 19th century that gravitation needs a proper field theory. Once special relativity entered the scene, it was well understood that a relativistic field theory was needed. And finally, as Einstein began investigating the notion of generalizing his relativity theory to treat accelerating frames on the same level as inertial frames (hence the name, general relativity, to expand on what was back then known simply as the theory of relativity, without the “special” adjective), the weak equivalence principle made him realize that such a theory must necessarily be a theory of gravitation.

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